Sensorless Field Oriented Control of 3-Phase Permanent ...

1 ApplicationReportSPRABQ3 July2013 SensorlessFieldOrientedControlof3-PhaseP ermanentMagnetSynchronousMotorsBilalAkin andManishBhardwajABSTRACTT hisapplicationreportpresentsa solutiontocontrola permanentmagnetsynchronousmotor(PMSM) , ,it is possibletorealizefarmoreprecisedigitalve ctorcontrolalgorithmslikethefieldorienta tedcontrol(FOC).Thisalgorithm simplementationis widerangeofspeedsandtakesintoconsiderati ontorquechangeswithtransientphasesbyproc essinga : A theoreticalbackgroundonfieldorientedmoto rcontrolprinciple Incrementalbuildlevelsbasedonmodularsoft wareblocks (FOC).. ControllersforDigitalMotorControl(DMC).. 107 TILiteratureandDigitalMotorControl(DMC) ( ).. Three-PhaseSynchronousMotorWitha ,andtheRotorFluxProducesa (FluxandTorqueareIndependentlyControlled andtheCurrentThroughtheRotorWindingsDete rminesHowMuchTorqueis Produced).

2 44 StatorCurrentSpaceVectorandItsComponenti n (a,b,c)..65 StatorCurrentSpaceVectorandItsComponents in ( , ) andin thed, ,VoltageandRotorFluxSpaceVectorsin thed,qRotatingReferenceFrameandTheirRela tionshipWitha,b,cand( , ) , July2013 SensorlessFieldOrientedControlof3-PhaseP ermanentMagnetSynchronousMotorsSubmitDoc umentationFeedbackCopyright 2013, ,Ta,Tb, ,Tb, - andB Voltagesbyvolt1 Module, , ,andPhaseA andB - ,MeasuredthetaandPhaseA andB - ,Estimatedtheta(SMO), - andB Currents,CalculatedPhaseA voltage , andB Currents,CalculatedPhaseA voltage , - brushlessPMSM hasa woundstator,a permanentmagnetrotorassembly, ,efficientheatdissipation, ,theeliminationofbrushesreducesnoise, solutiontocontrola ,consistingoffewersystemcomponents, a July2013 SynchronousMotorsSubmitDocumentationFeed backCopyright 2013, is ,therefore, motordimensionswhilemaintaininga Three-PhaseSynchronousMotorWitha OnePermanentMagnetPairPoleRotor3 SynchronousMotorOperation ,thestatorwindingscreatea ,it is necessarytocontrolthestatorcurrents.

3 ,therotorusuallyconsistsofwindingsin whicha designedforthenumberofdesiredpoles,andth edesiredfluxgradients. Theinteractionbetweenthestatorandrotorfl uxesproducesa firmlymountedtotheframe,andtherotoris freetorotate,therotorwillrotate,producin ga usefulmechanicaloutput. finetuningis neededafterclosingthespeedloopusingthese nsorlessalgorithmin ordertodrawtheminimumamountofcurrentunde rthesamespeedandtorqueconditions. Therotatingstatorfieldmustrotateatthesam efrequencyastherotorpermanentmagneticfie ld;otherwise, lessthanoptimaltorqueproduction,andexces sivemechanicalvibration,noise, ,if therotorinertiapreventstherotorfrombeing abletorespondtotheseoscillations,theroto rstopsrotatingatthesynchronousfrequency, phenomenonknownas pull-out . Thisis alsothereasonwhythesynchronousmachineis notselfstarting.

4 Theanglebetweentherotorfieldandthestator fieldmustbeequalto90 ordertogeneratetherightstatorfield. July2013 SensorlessFieldOrientedControlof3-PhaseP ermanentMagnetSynchronousMotorsSubmitDoc umentationFeedbackCopyright 2013,TexasInstrumentsIncorporatedArmatur e CircuitUeie( )FInductor (fieldexcitation)(E, R)TemUMT= K..= f(I )emeFF WF= K..IEWR otor FieldStator fieldA BC AB CNSFFF ieldOrientedControl(FOC) ,andtheRotorFluxProducesa TorqueThatCausestheMotortoRotate4 FieldOrientedControl(FOC) ,a ,advancedcontrolstrategiescanbeimplement ed,whichusesmathematicaltransformationsi n ordertodecouplethetorquegenerationandthe magnetizationfunctionsin commonlycalledrotorfluxorientedcontrol, ,startwithanoverviewoftheseparatelyexcit eddirectcurrent(DC) ,theexcitationforthestatorandrotoris (themagnitudeofthefieldexcitationcurrent ) incontactwiththebrushes,andthemechanical constructionis (FluxandTorqueareIndependentlyControlled andtheCurrentThroughtheRotorWindingsDete rminesHowMuchTorqueisProduced)

5 ,thereis onlyonesourcethatcanbecontrolled,whichis , ,theonlysourceofpowerandmagneticfieldis ,asopposedtotheDCmotor, July2013 SynchronousMotorsSubmitDocumentationFeed backCopyright 2013,TexasInstrumentsIncorporated2iiiiab caa=++ismiR Sq YTBB emstatorrotor= (FOC)ThegoaloftheFOC(alsocalledvectorcon trol)onthesynchronousandasynchronousmach ineis toimitatetheDCmotor s , ,it is necessarytoengageseveralmathematicaltran sforms,andthisis turnimpliesthattheentirealgorithmcontrol lingthemotorcanbeexecutedata fastrate, ,a dynamicmodelofthemotoris accountedforandtheoverallqualityofcontro lis ,thetorqueproducedin thesynchronousmachineis equaltothevectorcrossproductofthetwoexis tingmagneticfields:Thisexpressionshowsth atthetorqueis maximumif thestatorandrotormagneticfieldsareorthog onal,meaningif youaretomaintaintheloadat90.

6 If youareabletoensurethisconditionallthetim e,if youareabletoorientthefluxcorrectly,youre ducethetorquerippleandensurea ,theconstraintis toknowtherotorposition:thiscanbeachieved witha notaccessible, ,thegoalis tomaintaintherotorandstatorfluxin quadrature;thegoalis toalignthestatorfluxwiththeq axisoftherotorflux,forinstance, ,thestatorcurrentcomponentin quadraturewiththerotorfluxis controlledtogeneratethecommandedtorque,a ndthedirectcomponentis somecasesforfieldweakening,whichhastheef fectofopposingtherotorflux,andreducingth eback-emf, basedonprojectionsthattransforma threephasetimeandspeeddependentsystemint oa twocoordinate(dandqcoordinates) structuresimilartothatofa :thetorquecomponent(alignedwiththeqco-or dinate)andthefluxcomponent(alignedwithd co-ordinate).AsFOCis simplybasedonprojections, everyworkingoperation(steadystateandtran sient) ,theFOCsolvestheclassicschemeproblemsin thefollowingways: Theeaseofreachingconstantreference(torqu ecomponentandfluxcomponentofthestatorcur rent) Theeaseofapplyingdirecttorquecontrolbeca usein the(d,q)referenceframetheexpressionofthe torqueis:Bymaintainingtheamplitudeofther otorflux( R) ata fixedvalue,youhavea linearrelationshipbetweenthetorqueandtor quecomponent(iSq).

7 ,currents,andfluxesoftheAC-motorscanbean alyzedin , ,ib, icaretheinstantaneouscurrentsin thestatorphases,thecomplexstatorcurrentv ectoris definedby:5 SPRABQ3 July2013 SensorlessFieldOrientedControlof3-PhaseP ermanentMagnetSynchronousMotorsSubmitDoc umentationFeedbackCopyright 2013,TexasInstrumentsIncorporated1233iis aiiisabab= =+ cba=aiSabiSiSbciaaa2icaibbiS23jeaP=423je aP=FieldOrientedControl(FOC) , (a,b,c)where,(a,b,c) stillneedstobetransformedintoa : (a,b,c) ( , ) (theClarketransformation),whichoutputsa twocoordinatetimevariantsystem ( , ) (theClarketransformation),whichoutputsa (a,b,c) ( , ) Projection(ClarkeTransformation)Thespace vectorcanbereportedin anotherreferenceframewithonlytwoorthogon alaxiscalled( , ).Assumingthataxisa andaxis arein thesamedirection, ( , ) twodimensionorthogonalsystemispresentedb elow:Thetwophase( , ) July2013 SynchronousMotorsSubmitDocumentationFeed backCopyright 2013,TexasInstrumentsIncorporatedcossins incosiiisdssiiisqssqqabqqab=+ -+ ba= (FOC) ( , ) (d,q)Projection(ParkTransformation)Thisi s themostimportanttransformationin ,thisprojectionmodifiesa twophaseorthogonalsystem( , ) in thed, youconsiderthed axisalignedwiththerotorflux,Figure6 shows,forthecurrentvector, ( , ) andinthed,qRotatingReferenceFramewhere, is :Thesecomponentsdependonthecurrentvector ( , ) componentsandontherotorfluxposition;if youknowtherightrotorfluxpositionthen,byt hisprojection,thed,qcomponentbecomesa (time-invariant).

8 Atthispoint,thetorquecontrolbecomeseasie rwhereconstantisd(fluxcomponent)andisq(t orquecomponent) July2013 SensorlessFieldOrientedControlof3-PhaseP ermanentMagnetSynchronousMotorsSubmitDoc umentationFeedbackCopyright 2013,TexasInstrumentsIncorporatedqPIPISV PWMVDCVS refaVS refb3-phaseInvertera b,a b,d,qa,bClarke Park ,qa b, andis . Thesetwocomponentsofthecurrentaretheinpu tsoftheParktransformationthatprovidethec urrentin thed, (thefluxreference)andisqref(thetorqueref erence).Atthispoint,thiscontrolstructure showsaninterestingadvantage:it synchronouspermanentmagneta motor ,therotorfluxis fixeddeterminedbythemagnets; ,whencontrollinga PMSM, rotorfluxcreationin ordertooperate, classic ; refandVs ref, whicharethecomponentsofthestatorvectorvo ltagein the( , ) (synchronousorasynchronousmachine).

9 Therotorfluxpositionconsiderationsaredis cussedin ,if thereis anerrorin thisvariabletherotorfluxis showsthe(a,b,c),( , ) and(d,q) referenceframes,andthecorrectpositionoft herotorflux,thestatorcurrentandstatorvol tagespacevectorthatrotateswithd, July2013 SynchronousMotorsSubmitDocumentationFeed backCopyright 2013,TexasInstrumentsIncorporatedba= ,VoltageandRotorFluxSpaceVectorsinthed,q RotatingReferenceFrameandTheirRelationsh ipWitha,b,cand( , ) StationaryReferenceFrameThemeasureofther otorfluxpositionis differentif youconsidersynchronousorasynchronousmoto rs: Inthesynchronousmachine,therotorspeedis (rotorfluxposition)is directlymeasuredbypositionsensororbyinte grationofrotorspeed. Intheasynchronousmachine,therotorspeedis notequaltotherotorfluxspeed(thereis a slipspeed),thenit needsa particularmethodtocalculate.

10 Thebasicmethodis theuseofthecurrentmodelwhichneedstwoequa tionsofthemotormodelind, , , resultofthistransformation(socalledParkt ransformation),theq-axiscurrentwillbecon trollingthetorquewhilethed-axiscurrentis ,thekeymoduleofthissystemis July2013 SensorlessFieldOrientedControlof3-PhaseP ermanentMagnetSynchronousMotorsSubmitDoc umentationFeedbackCopyright 2013,TexasInstrumentsIncorporatedwr*wrPI iSqrefiSqPIPIiSdref++iSdVSqrefVSdrefInv. refbVS VoltageReconstructionPMSMTMS320F2803xSli ding-ModeBasedRotorPositionEstimatorSpee dCalculatorBased onEstimatedRotorPositionqqqiSaiSbVSaVSbi SaiSb* Reference variable+Benefitsof32-BitC2000 ControllersforDigitalMotorControl(DMC) depictedin ControllersforDigitalMotorControl(DMC)Th eC2000familyofdevicespossesthedesiredcom putationpowertoexecutecomplexcontrolalgo rithmsalongwiththerightmixofperipheralst ointerfacewiththevariouscomponentsoftheD MChardwareliketheanalog-to-digitalconver ter(ADC),enhancedpulsewidthmodulator(ePW M),QuadratureEncoderPulse(QEP),enhancedC apture(ECAP), , (librariesandapplicationsoftware)andhard ware(applicationkits)